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I just get into the graduated school and professor gives me this
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I just get into the graduated school and professor gives me this review question. I totally forget about all the knowledge I learnt and don't even know how to approach the question. Would some one help me with this L-C-R circuit? thanks a lot. please see detail in attachment. 


Part I.

 


 

Energy transfer (100 points)

 


 

IL

 

V1

 


 

V2

 


 

Figure 1.

 

Observe the circuit in Figure 1. Initial conditions: Voltage on C1 is v1(t = 0) =V1, on C2 is v2(t = 0) =V2,

 

V1 > V2, switch SW is open. At t = 0 sec SW is closed.

 

a) What is the characteristic frequency, f, (2 f = ) of oscillation of this circuit? (5p).

 

b) Define the quality factor, Q, for this circuit (5p).

 

c) Calculate the energy dissipated in R, assuming capacitances C1 and C2 are equal, and initial voltage

 

on C2 is zero for t > ?large?. How long time t is ?large? in this context (Give an inequality for t)? (25p)

 

d) How does the energy dissipated depend on R? (5p)

 

e) What is the maximum current, iLmax, in the inductor L in terms of circuit parameters C1, C2, R, L, and

 

initial voltages V1, V2 assuming R is zero. What is iLmax if R is ?small?, but not zero? (15p)

 

f) What are the maximum and minimum voltages on C2 in terms of circuit parameters and initial

 

voltages assuming R is zero. What are the sequence of peak voltages on C2 if R is ?small?, but not zero?

 

(20p)

 

g) Assume V2 = -V1 initially. What is the relation between C1 and C2 if at some instance of time t > 0

 

all energy is stored in C2 alone assuming R is zero? (20p)

 

h) What is the shortest time, t, at which this would occur? (5p)

 


 

1

 


 

 







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